Question

if the percentage increse in the area of circle is 44% what will be the percentage increase in its circumference?​

Answer 1

Answer:

Area of smaller circle = pix r^2

Area of larger circle = 1.44 pi x r^2 = pi x(1.2r)^2

So the radius should be increased by 20 percent to have a circle with an area increased by 44 percent.

Answer 2

❐ FULL EXPL@NATION:

.

Let The radius(r) of Circle be x.

As We Know That,

Area of Circle = π × r²

So,

• The Area of Circle = πx²

Circumference of Circle = 2πr

So,

• The Circumference of Circle = 2πx

After Increasing,

• ❥ Area of Circle = πx² + πx² × 44/100
• ❥ Area of Circle = πx² [1 + 11/25]
• ❥ Area of Circle = πx² [36/25]
• ❥ Area of Circle = π {x[6/5]}²
• ❥ π × R² = π (6x/5)²

[Comparing both sides]

• ❥ R = 6x/5

So,

• The New radius is 6x/5.

As We Know That,

• ❥ Circumference of New Circle = 2πR
• ❥ Circumference of New Circle = 2π × 6x/5
• ❥ Circumference of New Circle = 12πx/5

So,

• The Circumference of New Circle is 12πx/5.

As We Know That,

• ❥ Increase Percentage = Difference/Old Value × 100
• ❥ Increase Percentage = (12πx/5 - 2πx)/2πx × 100
• ❥ Increase Percentage = [(12πx - 10πx)/2πx] / 2πx × 100
• ❥ Increase Percentage = 2πx/5 × 1/2πx × 100
• ❥ Increase Percentage = 1/5 × 100
• ❥ Increase Percentage = 20%

So,

• The Increase Percentage in Circumference of Circles is 20%.

❐ REQUIRED ANSWER:

• The Increase Percentage in Circumference of Circles is 20%.